Question: Let X1, . . . , Xn be a random sample from the Poisson distribution with mean . Let Y = a. Prove that there

Let X1, . . . , Xn be a random sample from the Poisson with mean θ. Let Y =
a. Prove that there is no unbiased estimator of 1/θ. (Write the equation that is equivalent to Eθ (r(X)) = 1/θ. Simplify it, and then use what you know from calculus of infinite series to show that no function r can satisfy the equation.)
b. Suppose that we wish to estimate 1/θ. Consider r(Y) = n/(Y + 1) as an estimator of θ. Find the bias of r(Y), and show that the bias goes to 0 as n → ∞.
c. Use the delta method to find the asymptotic (as n→ ∞) of n/(Y + 1).

Step by Step Solution

★★★★★

3.45 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The distribution of Y is the Poisson distribution with mean n In order for rY to be an unb... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

602-M-S-S-D (2334).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

A function y = f(x) is defined as follows: y = f(x) 1.0 1.025 1.049 1.072 Compute the values of dyldx and vidr at x =1.05. X 1.0 1.05 1.10 1.15 X 1.20 1.25 1.30 y = f(x) 1.095 1.118 1.140

Let X1,..., Xn be a random sample from the pdf f(x|) = x-2, 0

Let X1,..., Xn be a random sample from the pdf f(x|) = e-(x-) where -

Statistics Question 1 Let X1, . .., Xn be a random sample from a Poisson distribution with mean 1. 1. Find the maximum likelihood estimator (MLE) of 1. 2. Determine whether the MLE is an unbiased...

Let X1,..., Xn be a random sample from the Poisson distribution with unknown mean . The uniformly minimum variance unbiased estimator (UMVUE) of exp() is known to be [(n 1)/n] Tn , where Tn = n i=1...

Let X1, . . . , Xn be a random sample from the Poisson distribution with mean . a. Express the Var(Xi) as a function 2 = g(). b. Find the M.L.E. of g() and show that it is unbiased.

(a) Let X1, . . ., Xn be a random sample from a Poisson distribution with parameter Î». Derive a (1 Î±) 100% large sample confidence interval for Î». (b) To date...

Let X1, . . ., Xn be a random sample from a Poisson distribution with parameter . Show that the sample mean X-bar is sufficient for .

Let X1, . . ., Xn be a random sample from a Poisson distribution with mean . Find a best critical region for testing H0: = 3 against Ha: = 6.

Let X1, . . ., Xn be a random sample from a Poisson distribution with parameter . (a) Construct a 90% confidence interval for . (b) Suppose that the number of raisins in a bowl of a particular brand...

What is simulation analysis, and how is it used?

Compute for the energy stored in a 10 F capacitor with a 25 mV across its terminals.

True or False? Because you can Undo edits, it is not necessary to make a backup copy of any data set before editing. Explain your answer.

Write an essay briefly summarizing property crimes. Address whether we still require the various property offenses that were developed by the common law.

Verify that (a) $z_{0.10}=1.28$ (b) $z_{0.001}=3.09$.

The burning time of an experimental rocket is a random variable having the normal distribution with $\mu=4.76$ seconds and $\sigma=0.04$ second. What is the probability that this kind of rocket...

Referring to Exercise 5.112, suppose the rotation speed of the coil can be increased and standard deviation decreased. Determine the new value for the standard deviation that would restrict the...

5. Red Buckle Inns plans to issue $85,000,000 of 20-year semi-annual bonds in January to help finance an expansion including 120 new hotels. It is now September, and the current cost of debt to the...

A mining company is considering a new project. Because the mine has received a permit, the project would be legal; but it would cause significant harm to a nearby river. The firm could spend an...

1 . In learning unit 1 you are introduced to a variety of policy and legislative measures in managing public finance. In your view, which one of these measures is themost important guidelinefor a...